Suppose 𝑓(𝑥) is a function whose graph is a TANGENT curve with the following features 1. Vertical Stretching = 15/16 2. Period = 𝜋 3. Phase shift = 0. 4. Midline 𝑦=0

Question

Using the trig function tan(x) , find an equation for the graph of f(x)

Answer 1

The function tan(x) has the following properties:

1. vertical scale of 1
2. period 2π
3. phase shift 0
4. midline: y = 0

In order to modify the tan(x) function to obtain the desired features of f(x), we must: 1) change the vertical stretching factor, 2) modify the period of the function, and 3) shift the phase. Note that no vertical shifts are required since the midline of tan(x) is the same as f(x).

We will make the following changes in order to find f(x):

1) multiply the outside of the tan(x) function by 15/16 to obtain the proper vertical stretching,

2) multiply the inside of the tan(x) function by 2 to obtain the proper period, and

3) add 0.4 on the inside of the tan(x) function to obtain the proper phase shift.

All of these steps put together gives the following result for f(x):

f(x) = 15/16 * tan(2x + 0.4)